Emergence of high piezoelectricity from competing local polar order-disorder in relaxor ferroelectrics

Relaxor ferroelectrics are known for outstanding piezoelectric properties, finding a broad range of applications in advanced electromechanical devices. Decoding the origins of the enhanced properties, however, have long been complicated by the heterogeneous local structures. Here, we employ the advanced big-box refinement method by fitting neutron-, X-ray-based total scattering, and X-ray absorption spectrum simultaneously, to extract local atomic polar displacements and construct 3D polar configurations in the classical relaxor ferroelectric Pb(Mg1/3Nb2/3)O3–PbTiO3. Our results demonstrate that prevailing order-disorder character accompanied by the continuous rotation of local polar displacements commands the composition-driven global structure evolution. The omnidirectional local polar disordering appears as an indication of macroscopic relaxor characteristics. Combined with phase-field simulations, it demonstrates that the competing local polar order-disorder between different states with balanced local polar length and direction randomness leads to a flattening free-energy profile over a wide polar length, thus giving rise to high piezoelectricity. Our work clarifies that the critical structural feature required for high piezoelectricity is the competition states of local polar rather than relaxor.


Methods:
Sample Preparation. Pb(Mg1/3Nb2/3)O3-xPbTiO3 (20  x  45) was prepared via solidstate route. The analytical reagent PbO, TiO2, Nb2O5 and MgO powders were selected as raw materials. The homogeneous mixture powders were calcined at 850 °C for 4 h, and then sintered at 1225 °C for 2 h. The ceramics were crushed into fine powder and annealed at 400 °C for 2 h to relive the residual stresses for neutron and X-ray total scattering and Extended x-ray absorption fine structure (EXAFS) measurements.
Total Scattering Measurements. The neutron total scattering data were collected at room temperature at Nanoscale-Ordered Materials Diffractometer (NOMAD) at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory. Approximately 1.5 g powder was placed in quartz capillary. The high quality data with Qmax about 35 Å -1 were reduced using ADDIE software. The pair distribution function G(r) were Fourier transformed from the corrected total scattering structure factors S(Q). X-ray total scattering was measured at the 11-ID-C beamline of the Advanced Photon Source (APS, Argonne National Laboratory) using an incident-beam energy of ≈115 keV with the area detector positioned at 320 mm away from the sample. The sample was loaded in quartz capillary. The X-ray data were processed using the PDFGetX3 software, 1 to obtain the corresponding total-scattering function and its Fourier transform with Qmax = 22 Å −1 . The NIST Si SRM powder total scattering data were collected to identify the instrument resolution in both X-ray and neutron total scattering measurements. The calculated total-scattering data were corrected for the instrument resolution in both reciprocal and real spaces 2 .
High Resolution Synchrotron X-ray Diffraction Measurements. The high resolution synchrotron X-ray diffraction were conducted at 11-BM-B beamline of APS with a wavelength of 0.45 Å. The powder samples were placed in a 0.3 mm diameter kapton capillary that was spun during the experiments. The diffractometer uses multiple singlecrystal analyzer detectors to offer high-resolution (ΔQ/Q < 1.410 -4 ) data collection. EXAFS experiments. The EXAFS of the Pb LIII-edge (13.035 keV) were performed at the 20-BM-B beamline at APS (Argonne National Laboratory). The X-ray absorption coefficient was measured in transmission mode as a function of the incident photon energy. The raw x-ray absorption spectrum processing and initial fitting were conducted on Athena and Artemis software 3,4 . Scattering amplitudes and phases were estimated using FEFF8 5 . The k-space data were multiplied by k-weight of 1, 2 and 3 and the kspace range used in the Fourier transform was 2.1 Å −1 to 8-10 Å −1 , while the r-space fit was conducted from 1 Å to 3.5 Å, with single-scattering paths included. The data and fit range results in about 162 independent point each measurement. The Pb-O scattering paths were characterized by bond length determined from the big-box refinement. The high-quality Pb LIII-edge EXAFS data are typically difficult to collect. Considering the quality of EXAFS data, during the RMC fitting, the actual weight factor of Pb LIII-edge EXAFS data is smaller than the N-/X-PDF data. polarization ⃗⃗ can be calculated by equation (3): To get the statistical analysis results about the polar displacement, four refined 3D atom configurations were merged together.
Phase-field simulations. Phase field modeling of PMN-PT are used to investigate the composition-dependent evolution of domain structures and piezoelectric response d33.
The domain structures are described by the spatial distribution of spontaneous polarization P (P1, P2, P3). The temporal evolution of the polarization is described by the time-dependent Ginzburg-Landau (TDGL) equation, the displacement field u and electric displacement field D are solved with the stress/electric equilibrium equation 8 Here, L is a kinetic coefficient related to domain wall mobility, F is the total free energy of the system, is the thermodynamic driving force for polarization evolution, σij is the stress tensor , f is the free charge density. r and t are the spatial coordinate and time, respectively. The total free energy of a bulk system can be defined as follows, Here, F includes the bulk free energy The bulk free-energy density is expressed for zero strain as a six-order polynomial expansion, that is where αi, αij, αijk are the Landau parameters. The elastic energy density can be written where Cijkl is the elastic stiffness tensor, εij is the total strain and εij 0 is the eigenstrain. The eigenstrain can be described as where Qijkl is the electrostrictive coefficient. The gradient energy density can be obtained by fgrad = Here, a random electric field that obeys the Gaussian distribution (0, ∆) was applied to account for the ERF, where ∆ is the variance of the Gaussian distribution.
Based on the random field theory for relaxors, local random fields are introduced to characterize the effect of chemical disorder. With PT doping from x=0.2 to x=0.45, the random local electric field variance decreased from 30 kV/mm to zero. During modeling, two effects are employed. Firstly, composition-induced MPB will lower the energy barrier compared with the single R/T phase, which is supposed to lead to a maximum d33 value in MPB. However, the calculated d33 from phase-field method will not decrease with decreased x value (x < 0.33), which may originate from the low energy barrier in the R phase. Secondly, the increased randomness of polar order parameters is characterized by an increase in random local electric field variance. With the random field effect, the calculated d33 decreased to ~233 pC/N (x = 0. EXAFS data are typically difficult to collect. The quality of EXAFS data in present study are comparable with previous reported in the literatures 10,11 . Considering the quality of EXAFS data, during the RMC fitting, the actual weight factor of Pb LIII-edge EXAFS data is smaller than the neutron and X-ray PDF data.  from MPB-to-R, which is completely different with the PZT system. This arises from the relaxor feature. Specifically, for MPB composition PZT53, the polar disorder is from the multiphase coexistence, and leads to a less polar disorder (disorder parameter  = 0.25). In PMN-PT system, the polar disorder is not only from the multiphase coexistence, but also from the existence of relaxor feature (disorder parameter  = 0.5 in 30PT). The existence of relaxor feature leads to higher degree disorder polar direction in PMN-30PT compared with conventional PZT53. Macroscopically, the PMN-PT system displays much higher piezoelectric response (d33  700 pC/N) compared with PZT system (d33  220 pC/N). Therefore, the mechanism of competing of local polar order-disorder is beyond the multiphase coexistence. The multiphase coexistence cannot rationalize the scenario that relaxor systems present several times higher piezoelectric coefficients compared to classical ferroelectric counterparts. Cmaprsion of the domain structures calculated from phase-field simulation between with (a) and without (b) introducing random electric fields. In the phase-field simulations, random electric field are commonly used to simulate the relaxor behavior in relaxors due to the chemcial disorder 12,13 . Without introducing random electric field, one can not get the correct Landau energy profiles, and thus unable to get the correct domain strcutres and piezoelctirc response. One can clearly see that the domain structures are completely different between these with introduction of random electric field (consider as disorder) and these without. The local polar direction randomness